If this is correct, it means the Sony PlayStation 4 has substantially outsold its rival. In March, Andrew House, president and CEO of Sony Computer Entertainment, said Sony had sold 36 million PS4 consoles since it launched in November 2013.
Microsoft, meanwhile, has not issued a sales figure update since November 2014. The company did not respond to requests for comment at the time of publication.
However, Gfinity later said that it did not have access to Microsoft's sales figures and was basing its estimates on other source.
"Gfinity would like to clarify that it has not sought to confirm Microsoft sales figures," the company said in a statement to CNBC. "The comments in yesterday's statement are based on a variety of independent sources published earlier this year."
The figure of 18 million tallies with previous estimates made by different individuals, including Electronic Arts CFO Blake Jorgensen who, during a financial conference in January, implied that around 18 to 19 million Xbox consoles had been sold.